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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 28th 2014

    we were lacking an entry realizability that points to all the related entries (and in fact some entries were asking for just “realizability”).

    So I started one. Put in the following Idea-paragraph:

    The idea of realizability is essentially that of constructivism, intuitionistic mathematics and the propositions as types paradigm: for instance constructively a proof of an existential quantification xXϕ(x)\underset{x\in X}{\exists} \phi(x) consists of constructing a specific xXx \in X and a proof of ϕ(x)\phi(x), which “realizes” the truth of the statement, whence the name (e.g. Vermeeren 09, section 1).

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeFeb 28th 2014

    added some more canonical references

  1. Added a reference to Andrej’s lecture notes.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMar 1st 2014
    • (edited Mar 1st 2014)

    Thanks! I already had this with more bibliographic information at computable analysis, but without the link to a pdf copy. Have merged the information now to:

    Andrej Bauer, Realizability as connection between constructive and computable mathematics, in T. Grubba, P. Hertling, H. Tsuiki, and Klaus Weihrauch, (eds.) CCA 2005 - Second International Conference on Computability and Complexity in Analysis, August 25-29,2005, Kyoto, Japan, ser. Informatik Berichte, , vol. 326-7/2005. FernUniversität Hagen, Germany, 2005, pp. 378–379. (pdf)

    Also added this citation to constructive mathematics and to computability and cross-linked a bit more.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMar 4th 2014

    Upon request, Andrej Bauer kindly made available his text

    • Intuitionistic Mathematics and Realizability in the Physical World (web, pdf)
    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 10th 2020
    • (edited Dec 10th 2020)

    added the full publication data for

    diff, v18, current

  2. updated link to Martin Hyland pdf


    diff, v21, current